A screeding test which measures the level of a prostate specic antigen (PSA) is a commonly used tool for the detection of prostate cancer. Men with PSA levels greater than 10 (ng/ml) have on average a chance of 67 % of prostate cancer, whereas men whose PSA levels are between 4 and 10 have on average a 25 % chance of having prostate cancer. For those whose PSA levels are below 4 %, the average risk of developing prostate cancer is only 5 %. Suppose that 15 % of men have PSA levels greater than 10, 10 % of men have PSA levels between 4 and 10, and 75 % of men have PSA levels lower than 4.
(a) What is the probability that a randomly chosen man will develop prostate cancer?
(b) What is the probability that a randomly chosen man has a PSA level greater than 10, given that he has prostate cancer?